The interfacial Dzyaloshinskii-Moriya interaction (DMI) is of great interest as it can stabilize chiral spin structures in thin films. Experiments verifying the orientation of the interfacial DMI vector remain rare, in part due to the difficulty of separating vector components of DMI. In this study, Fe/Ni bilayers and Co/Ni multilayers were deposited epitaxially onto Cu(001) and Pt(111) substrates, respectively. By tailoring the effective anisotropy, spin reorientation transitions (SRTs) are employed to probe the orientation of the DMI vector by measuring the spin structure of domain walls on both sides of the SRTs. The interfacial DMI is found to be sufficiently strong to stabilize chiral Neel walls in the out-of-plane magnetized regimes, while achiral Neel walls are observed in the in-plane magnetized regimes. These findings experimentally confirm that the out-of-plane component of the DMI vector is insignificant in these fcc(001) and fcc(111) oriented interfaces, even in the presence of atomic steps.